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Constructs infinitely many symmetry orders with smooth star-shaped non-disk counterexamples through a uniform bifurcation argument.
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Constructs infinitely many symmetry orders with smooth star-shaped non-disk counterexamples through a uniform bifurcation argument.
Passage ID: schiffer-pompeiu:entry:bifurcation:v1
Source item: bifurcation
Source record: schiffer-pompeiu:source:bifurcation:v1
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Problem publication v7
Source assessment
Proved
Infinite family of smooth counterexamples proved in the cited paper
Infinitely many integers N ≥ 2; bounded simply connected star-shaped C∞ domains with N-fold symmetry.
Source date Aug 5, 2026 · Observed Oct 13, 2026
Scope
Infinitely many smooth symmetry orders
History
An infinite family by uniform bifurcation
History
Pompeiu asks whether domain averages determine a function
Question
Schiffer and Pompeiu conjectures
Further reading
Read the mathematical argument; inspect its Claim for assessment and scope.
Recorded authorship
Gonzalo Cao-Labora · Jaume de Dios Pont
Gonzalo Cao-Labora, Jaume de Dios Pont
The authors credit GPT-5.5/5.6 and Claude Opus 4.8/Fable 5 for exploration, checks and exposition; GPT-5.6 assisted the early-draft Lean verification. The authors retain responsibility.
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Counterexamples to Schiffer’s Conjecture
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